Given: The function
[tex]y=3(x+4)^2+5[/tex]To Determine: The equivalent function of the given function
Solution:
Step 1: Expand the parenthesis
[tex]\begin{gathered} y=3(x+4)^2+5 \\ (x+4)^2=(x+4)(x+4) \\ (x+4)^2=x(x+4)+4(x+4) \\ (x+4)^2=x^2+4x+4x+16 \\ (x+4)^2=x^2+8x+16 \end{gathered}[/tex]Step 2: Substitute the expanded into the function
[tex]\begin{gathered} y=3(x+4)^2+5 \\ y=3(x^2+8x+16)+5 \\ y=3x^2+24x+48+5 \\ y=3x^2+24x+53 \end{gathered}[/tex]Hence, the equivalent function to the given is y = 3x²+24x+53, OPTION C
change these to decimals. 7%, 200%, .3%
the 7% means
7/100 = 0.07
[tex]7\text{ \% =}\frac{7}{100}=0.07[/tex]200 % means
200/100 = 2
and 0.3 % means
0.3/100 = 0.003
Solve the following quadratic equation using the quadratic formula in the picture: Problem: -3y^2 - 2y - 6 = 0
The given equation is,
[tex]-3y^2-2y-6=0[/tex]Here, a = -3, b = -2, c = -6. Therefore, y can be calculated as,
[tex]\begin{gathered} y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{2\pm\sqrt[]{4-(4)(-3)(-6)}}{-6}=-\frac{1\pm\sqrt[]{-68}}{3} \\ =\frac{-1+\sqrt[]{68}}{3},\frac{-1-\sqrt[]{68}}{3} \end{gathered}[/tex]Give the slope and the Y intercept of the line represented by y-7=-7x
Answer:
• m=-7
,• b=7
Explanation:
Given the line:
[tex]y-7=-7x[/tex]To determine the slope and y-intercept, first, express the line in the slope-intercept form (y=mx+b).
[tex]\implies y=-7x+7[/tex]You can then compare:
• Slope, m = -7
,• y-intercept, b =7
The slope of the line is -7 and the y-intercept is 7.
FIRST ANSWER WILL GET BRAILIEST! AND 50 PTS!
Which division problem is represented with this model?
Responses
1/5÷6
1/6÷2
1/2÷5
1/5÷2
Answer: Choice B
1/6÷2
Reason:
We have 6 slips of paper side by side. Shading one of those 6 represents the fraction 1/6.
Then split that shaded piece of paper in half as shown in the diagram. The blue region in that diagram represents 1/6÷2 which simplifies fully to 1/12.
If you were to do this to all 6 pieces of paper, then we'd have 2*6 = 12 smaller pieces. One of which is shaded, so that explains how we get 1/12.
In other words:
[tex]\frac{1}{6} \div 2 = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}[/tex]
identify the correct trigonometry formula to use to solve for the given anglea. sin-¹(1.41)b. cos-¹(1.41)c. sin-¹(.71)d. tan-¹(.71)
The definition of arctan is opposit side by adjesent side.
[tex]\begin{gathered} \text{Angle}=tan^{-1}(\frac{Oppos\text{ side}}{\text{Adjesent side}}) \\ =\tan ^{-1}(\frac{34}{48}) \\ =\tan ^{-1}(0.71) \end{gathered}[/tex]Thus, the correct option is option d.
Are the pair of lines y = 1/3x - 1 and y = 3x parallel, perpendicular, or neither?
A line with slope m and y-intercept b has the following slope-intercept form equation:
[tex]y=mx+b[/tex]If two lines have the same slope, they are parallel. If they have slopes that are the negative reciprocal of each other, then they are perpendicular.
If none of the above cases happen, then they are neither parallel nor perpendicular.
The line y = (1/3)x - 1 has slope 1/3.
The line y = 3x has slope 3.
As we see, the slopes are different, so the lines are not parallel. Also, the negative reciprocal of 3 is -1/3, not 1/3.
Therefore, the given lines are neither parallel nor perpendicular.
What plus Ten equals thirty two
What plus Ten equals thirty two is equivalent to
x + 10 = 32
10 is adding on the left, then it will subtract on the right
x = 32 - 10
x = 22
a chemical company makes two brands of antifreeze. the first brand is 45% pure antifreeze and the second brand is 70% pure antifreeze. in order to obtain 170 gallon of a mixture that contains 65% pure antifreeze how many gallons of each brand of antifreeze mudt be used
Answer:
The first brand is 34 gallons
The second brand is 136 gallons
Explanation:
Let x represent the first brand, and
y represent the second brand
The total number of gallons of mixture to be obtained is 170, so
x + y = 170 .................................................................................(1)
And
45% of x + 70% of y = 65% of (x + y)
0.45x + 0.7y = 0.65(x + y)
0.45x - 0.65x = 0.65y - 0.7y
0.2x = 0.05y
Divide both sides by 0.05
4x = y ...........................................................................................(2)
Solving (1) and (2) simultaneously
Using (2) in (1)
x + 4x = 170
5x = 170
Divide both sides by 5
x = 170/5 = 34
Put x = 34 in (2)
4(34) = y
y = 136
What is the value of t? 76 T
Those are vertical angles, which are two non-adjacent angles formed by intersecting two lines. The intersection forms two pair of vertical angles. So:
[tex]m\angle t=76[/tex]A house addition is in the shape of a semicircle (a half-circle) with a radius of 9 ft. What is itsarea?
We find its area as follows:
[tex]A=\frac{1}{2}\pi r^2[/tex][This is the equation for the area of a circle divided by 2] Now, we replace the radius:
[tex]A=\frac{1}{2}\pi(9)^2\Rightarrow A=\frac{81}{2}\pi\Rightarrow A\approx127.23[/tex]So, the area of the semi-circle is approximately 127.23 squared feet.
Find the equation of the line containing the point (3,5) and having slope: 4A. y=4x+24B. y=4x+7C. y=4x+17D. y=4x
Data
Point = (3, 5)
slope = 4
Equation of a line
y - y1 = m(x - x1)
m = slope = 4
x1 = 3
y1 = 5
Substitution
y - 5 = 4(x - 3)
Simplifying
y - 5 = 4x - 12
y = 4x - 12 + 5
Result
y = 4x - 7
Dan is a software salesman. His base salary is $2200, and he makes an additional $120 for every copy of History is Fun he sells.Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 23 copies of History is Fun.
We will have the following:
The equation in this case is:
[tex]P=120N+2200[/tex]So, if he sells 23 copies, he will make:
[tex]P(23)=120(23)+2200\Rightarrow P(23)=4960[/tex]So, he would make $4960.
Edward deposited 9,000 into a savings account 2years ago tthe simple interest is 2% how much money did edward earn in intrest
We just need to use the simple interest formula:
[tex]I=PV\cdot r\cdot t[/tex]Where:
I = Interest
PV = Principal or initial investment = 9000
r = interest rate = 0.02
t = time = 2
[tex]\begin{gathered} I=9000\times0.02\times2 \\ I=360 \end{gathered}[/tex]$360
how does a to the 4 b to -5 over c to -3 d to the 6th get simplified?
Given the expression
[tex]\frac{a^4b^{-5}}{c^{-3}d^6}[/tex]To simplify the expression above, we convert all negative indices to positive indices
Applying the rule of indices
[tex]a^{-x}=\frac{1}{a^x}[/tex]Applying the rule to the given expression gives
[tex]\begin{gathered} \text{Where b}^{-5}=\frac{1}{b^5}\text{ and} \\ c^{-3}=\frac{1}{c^3} \end{gathered}[/tex]Substitute the above deduction into the given expression
[tex]\begin{gathered} \frac{a^4b^{-5}}{c^{-3}d^6}=a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6} \\ \text{Where }\frac{1}{\frac{1}{c^3}}=c^3 \\ =a^4\times\frac{1}{b^5}\times\frac{1}{\frac{1}{c^3}}\times\frac{1}{d^6}=a^4\times\frac{1}{b^5}\times c^3\times\frac{1}{d^6} \\ =\frac{a^4c^3}{b^5d^6} \\ \frac{a^4b^{-5}}{c^{-3}d^6}=\frac{a^4c^3}{b^5d^6} \end{gathered}[/tex]Hence, the simplified form is
[tex]\frac{a^4c^3}{b^5d^6}[/tex]62 - 12 ÷ 3 + (15-7)
62 - 12 ÷ 3 + (15-7)
First, solve the parenthesis:
62-12÷ 3 + 8
Then, solve the division:
62-4+8
Add And subtract
66
solve y=f(x) for x. then find the inputs when the output is -3
Answer:
Given that,
[tex]f(x)=-7x-2[/tex]To find the inputs when the output is -3
that is, when f(x)=-3, to find the value of x
Put f(x)=-3 in the above equation we get,
[tex]-3=-7x-2[/tex][tex]-7x=-3+2[/tex][tex]\begin{gathered} -7x=-1 \\ x=\frac{1}{7} \end{gathered}[/tex]Answer is: x=1/7.
which equation doesn't represent a linear function? [tex]a. \: y = \frac{1}{2}x \: + 2[/tex][tex]b . \: y = {x}^{2} \\ c . \: y = 2x \\ d. \: y = x - 2[/tex]
The general equation for linear equation is,
[tex]y=mx+b[/tex]The equation y = x^2, consist of power term on the variable x. So this equation does not follow the linear equation and is a quadratic equation.
Thus, equation y = x^2 is not a linear function. Option B is correct answer.
The school band brought cheese and pepperoni pizzas in ratio represented in the tape diagram for their end of year party.
ANSWER
2 pepperoni pizzas
EXPLANATION
From the tape diagram, the ratio of cheese pizzas to pepperoni pizzas is:
3 : 1.
They bought 6 cheese pizzas.
Let the number of pepperoni pizzas be x.
So, by comparison, we have that:
3 : 1 = 6 : x
or
[tex]\begin{gathered} \frac{3}{1}\text{ = }\frac{6}{x} \\ \text{Cross multiply to find x:} \\ 3\cdot\text{ x = 6 }\cdot\text{ 1} \\ \text{Divide through by 3:} \\ x\text{ = }\frac{6}{3} \\ x\text{ = 2} \end{gathered}[/tex]Therefore, they bought 2 pepperoni pizzas.
complete the function table for the given domain and plot the points on the graph f(x)=2^x-7x. 0. 1. 2. 3. 4. f(x) . . . . graph
we have the following:
[tex]f(x)=2^x-7[/tex]replacing:
[tex]\begin{gathered} f(0)=2^0-7=1-7=-6;(0,-6)^{} \\ f\mleft(1\mright)=2^1-7=2-7=-5;(1,-5) \\ f\mleft(2\mright)=2^2-7=4-7=-3;(2,-3) \\ f(3)=2^3-7=8-7=1;(3,1) \\ f(4)=2^4-7=16-7=9;(4,9) \end{gathered}[/tex]x 0 1 2 3 4
f(x) -6 -5 -3 1 9
The graph shows the distance Kendrick walks in different lengths of time.How many kilometers does Kendrick walk per hour?5kilometersHow long does it take Kendrick to walk 111 kilometer?hours
Solution
For this case we can do this:
[tex]\frac{10-5}{2-1}=\frac{5\operatorname{km}}{hr}[/tex]5 kilometers
We have the following equation
Km = m*hours
hours= 1km/ (5km/hr) =0.2hr
Which is a solution toy ⩽ -2x + 1 (-3,8)(2,-2)(0,5)(-1, 3)
To find the right solution, we just have to evaluate the expression with each given point
(-3,8)[tex]\begin{gathered} 8\leq-2\cdot(-3)+1 \\ 8\leq6+1 \\ 8\leq7 \end{gathered}[/tex](2,-2)[tex]\begin{gathered} -2\leq-2\cdot2+1 \\ -2\leq-4+1 \\ -2\leq-3 \end{gathered}[/tex](0,5)[tex]\begin{gathered} 5\leq-2\cdot0+1 \\ 5\leq1 \end{gathered}[/tex](-1,3)[tex]\begin{gathered} 3\leq-2\cdot(-1)+1 \\ 3\leq2+1 \\ 3\leq3 \end{gathered}[/tex]As you can observe, the last choice satisfies the inequality.
Hence, the answer is (-1,3).For each of the following letters, find the equation for a polynomial function whose graph resembles the given letter: U, N, M, and W.
We are asked to determine polynomic functions which graph resembles the given letters.
For the letter U we will use a second-degree polynomial, which means a polynomial of the form:
[tex]y=ax^2+b[/tex]Is we take the values of "a" and "b" to be:
[tex]\begin{gathered} a=1 \\ b=0 \end{gathered}[/tex]We get the function:
[tex]y=x{}^2[/tex]The graph is the following:
Now, to determine a function that resembles the letter N we will use a polynomic function of third-degree, this means a function of the form:
[tex]y=ax^3+bx^2+cx+d[/tex]We will use the following values for the constants:
[tex]\begin{gathered} a=\frac{1}{4} \\ \\ b=1 \\ c=0 \\ d=0 \end{gathered}[/tex]Substituting we get:
[tex]y=\frac{1}{4}x{}^3+x^2[/tex]The graph of the function is:
To determine a polynomial that resembles the letter "m" we will use a polynomial that has 3 x-intercepts and the end-points are pointing down. This means that the function is of the form:
[tex]y=-(x-a)(x-b)^2(x-c)[/tex]The middle term has a square because we want the middle intercept to be tangent to the x-axis. Giving values to the constant we get:
[tex]y=-(x+1)(x-1)^2(x-3)[/tex]The graph of the function is:
Now, we determine a function that resembles the letter "W". We will use a polynomial with two intercepts that are tangent to the x-axis and the end behavior must be upwards. Therefore, the function must be of the form:
[tex]y=(x-a)^2(x-b)^2[/tex]We will use a = -1 and b = 1:
[tex]y=(x+1)^2(x-1)^2[/tex]The graph is:
I'm confused about how to solve this using the special right triangles method
ANSWER:
[tex]x=4\sqrt[]{2}[/tex]STEP-BY-STEP EXPLANATION:
We can calculate the value of x, by means of the trigonometric function sine
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{opposite = }4 \\ \theta\text{ =60\degree} \\ \text{hypotenuse = x} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} \sin 45=\frac{4}{x} \\ x=\frac{4}{\sin45} \\ \sin 45=\frac{\sqrt[]{2}}{2} \\ x=\frac{4}{\frac{\sqrt[]{2}}{2}} \\ x=\frac{8}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ x=\frac{8\sqrt[]{2}}{2} \\ x=4\sqrt[]{2} \end{gathered}[/tex]Type the correct answer in each box. Use numerals instead of words. If necessary, use/ for the fraction bar(s).The equation of a circle is given.2+ y²+6x+10y+18=0Determine the center and radius of the circle.) and the radius of the circle isunits.The center of the circle is at (ResetNext
ANSWER
[tex]\begin{gathered} center=(-3,-5) \\ r=4 \end{gathered}[/tex]EXPLANATION
Given;
[tex]x^2+y^2+6x+10y+18=0[/tex]The standard equation of circle of a circle centered at (h,k) with radius r is;
[tex](x-h)^2+(y-k)^2=r^2[/tex]Re-write the given equation in the standard form, we have;
[tex]\begin{gathered} x^{2}+y^{2}+6x+10y+18=0 \\ x^{2}-6x+(\frac{6}{2})^{2}+y^{2}+10y+(\frac{10}{2})^{2}=-18+9+25 \\ (x-3)^2+(y-5)^2=4^2 \end{gathered}[/tex]Hence, h=-3, k=-5, radius is 4
which of the following are accurate of the distribution below
A: An outlier is a point that is an exception compared to the distribution of the data. In a histogram, it would appear as a bar away from the distribution with a lower height. We can't observe this in this distribution.
A do not apply.
B: A cluster is an accumulation of point in a certain interval. The interval given is 0 to 39. In the distribution, there are no points for this interval, so no cluster.
B do not apply.
Since A and B do not apply, C do apply.
7-Which beans are the better deal? O Kidney Beans $1.18 per Ib Lima Beans $2.13 for 2 lbs 7b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 07 00, so if answer is 43 cents, its 043 or 43, if there is a dollar amount ke 1.50, do not add zeros in front) Your answer
Kidney $1.18 per 500g
Lima. $ 2.13. Per 2 lbs= 1000g
Then
Kidney = 1.18 x 1 lb
Lima = 2.13/2= 1.065 x 1 lb
So ANSWER IS :Better deal Is LIMA BEANS
Part 7b
UNIT PRICE for better deal is
LIMA BEANS , At $1.065 per lb
One sample t for means You want to know if the average customer rating fro your store is about a 7.0 on a 1-10 scale. Your collect a sample of 100 customers. Their average rating was 7.3, with a standard deviation of 2.0.
Given:
A sample of 100 customers.
The circle is inscribed in the square. Find the area of the shaded region.
We can solve this by calculating the area of the square and subtracting the area of the inscribed circle. The area of the square is:
[tex]Square=10\cdot10=100cm^2[/tex]The formula for the area of a circle is:
[tex]A=\pi r^2[/tex]The radius of the inscribed circle is half the length of the side of the square, then, the radius is r = 5 cm
[tex]Circle=\pi5^2=25\pi\text{ }cm^2[/tex]Now, we rest:
[tex]Square-Circle=100cm^2-25\pi cm^2\approx21.46cm^2[/tex]The answer is 21.46cm²
The problem is:The area of a square picture frame is 55 square inches. Find the length of one side of the frame. explain.Part A. Part B To the nearest whole inch. To the nearest 10th of an inch
Part A
area = 55 in²
The area of a square is given by:
area = side x side
So
55 in² = side x side
55 in² = side²
Taking the square root of both sides of the equation we get:
√55 in² = side
7 in = side
Part B
side = 7.4 in
Suppose the main income of firms in the industry for a year is $80 million with a standard deviation of $13 million. If incomes for the industry are distributed normally what is the probability that a randomly selected firm will earn less than $96 million? Round your answer to four decimal places
Given that
The mean income of firms in the industry for a year is $80 million with a standard deviation of $13 million. and we have to find the probability that a randomly selected firm will earn less than $96 million.
Explanation -
We have to find the probability that a firm will earn less than $96 million.
The mean is $80 and the standard deviation is $13.
Then, it is written as
[tex]\begin{gathered} P(x<96)=P(z<\frac{96-80}{13}) \\ \\ The\text{ formula to find the z is \lparen here z is the z value\rparen} \\ z=\frac{x-\mu}{\sigma} \\ \mu\text{ is mean and }\sigma\text{ is the standard deviation.} \\ \\ P(<96)=P(z<\frac{16}{13})=P(z<1.2) \end{gathered}[/tex]The table to find the z value is
According to the z table, the value will be
[tex]\begin{gathered} P(x<96)=P(z<1.2)=0.8849 \\ P(x<96)=88.49\% \end{gathered}[/tex]Hence, 88.49% of the randomly selected firms will earn less than $96.
So the probability will be 0.8849.
Final answer -
The final answer is 0.8849 or 88.49%.